## Signal Processing

- The Fast Fourier Transform Algorithm, and Denoising a Sound Clip
- The Two-Dimensional Fourier Transform and Digital Watermarking
- Making Hybrid Images
- The Welch-Berlekamp Algorithm for Correcting Errors in Data

## Machine Learning and Data Mining

- Introduction
- K-Nearest-Neighbors and Handwritten Digit Classification The Perceptron, and All the Things it Can’t Perceive
- Decision Trees and Political Party Classification
- Neural Networks and the Backpropagation Algorithm
- K-Means Clustering and Birth Rates
- Linear Regression
- Regression and Linear Combinations
- Eigenfaces, for Facial Recognition (via Principal Component Analysis)
- Bandit Learning: the UCB1 Algorithm
- Bandit Learning: the EXP3 Algorithm
- Bandits and Stocks
- Weak Learning, Boosting, and the AdaBoost Algorithm
- Fairness in machine learning
- The Johnson-Lindenstrauss Transform
- Singular Value Decomposition
- Support Vector Machines

## Graphs and Network Science

- Binary Search on Graphs
- Trees and Tree Traversal
- Breadth-First and Depth-First Search
- The Erdős-Rényi Random Graph
- The Giant Component and Explosive Percolation
- Zero-One Laws for Random Graphs
- Community Detection in Graphs, a Casual Tour
- Google’s PageRank Algorithm: Introduction
- A First Attempt
- The Final Product
- Why It Doesn’t Work Anymore

## Combinatorial Optimization

- When Greedy is Good Enough: Submodularity and the 1 – 1/e Approximation
- When Greedy Algorithms are Perfect: the Matroid
- Linear Programming and Healthy Diets Part 1
- Linear Programming and the Simplex Algorithm
- Linear Programming and Healthy Diets Part 2
- The Many Faces of Set Cover
- Optimization Models for Subset Cover

## Art & Graphics

- Making Hybrid Images
- Bezier Curves and Picasso
- Random Psychedelic Art
- Seam-carving for Content-Aware Image Scaling
- The Cellular Automaton Method for Procedural Cave Generation
- Designing Non-repeating Patterns with Prime Numbers

## Algorithmic Game Theory

- Stable Marriages and Designing Markets
- Serial Dictatorships and Housing Allocation
- Silent Duels and an Old Paper of Restrepo
- Silent Duels—Parsing the Construction
- Silent Duels—Constructing the Solution part 1
- Silent Duels—Constructing the Solution part 2

## Software Engineering

## Quantum Computing

- A Motivation for Quantum Computing
- The Quantum Bit
- Multiple Qubits and the Quantum Circuit
- Concrete Examples of Quantum Gates

## Cryptography

- RSA
- Elliptic curves
- Introduction
- Elliptic Curves as Elementary Equations
- Elliptic Curves as Algebraic Structures
- Elliptic Curves as Python Objects (over the rational numbers)
- Programming with Finite Fields
- Connecting Elliptic Curves with Finite Fields
- Elliptic Curve Diffie-Hellman
- Sending and Authenticating Messages with Elliptic Curves (Shamir-Massey-Omura and ElGamal)

- The Mathematics of Secret Sharing
- Zero Knowledge Proofs
- Fully homomorphic encryption:
- A High-Level Technical Overview of Fully Homomorphic Encryption
- Fully Homomorphic Encryption in Production Systems
- The Gadget Decomposition in FHE
- Modulus Switching in LWE
- Key Switching in LWE
- Sample Extraction from RLWE to LWE
- Negacyclic Polynomial Multiplication
- Estimating the Security of Ring Learning With Errors
- Encoding schemes in FHE
- Shift Networks
- Packing Matrix-Vector Multiplication
- Google’s Fully Homomorphic Encryption Compiler (Tutorial)

## Streaming and Sublinear Algorithms

## Natural Language

## Computational Category Theory

- A Sample of Standard ML (and a Preview of Monoids)
- Categories, What’s the Point?
- Introducing Categories
- Categories as Types
- Properties of Morphisms
- Universal Properties
- Functoriality
- The Universal Properties of Map, Fold, and Filter

## Computational Topology

## Games

- The Wild World of Cellular Automata
- Turing Machines and Conway’s Dreams
- Conway’s Game of Life in Conway’s Game of Life
- Optimally Stacking the Deck: Kicsi Poker
- Optimally Stacking the Deck: Texas Hold ‘Em
- Want to make a great puzzle game? Get inspired by theoretical computer science
- Socks: a matching game based on an additive combinatorics problem

## Miscellaneous

- Two’s Complement and Group Theory
- Group Actions and Hashing Unordered Multisets
- A Working Mathematician’s Guide to Parsing
- A Quasipolynomial Time Algorithm for Graph Isomorphism: The Details
- The Reasonable Effectiveness of the Multiplicative Weights Update Algorithm
- Taylor Series and Accelerometers
- Hunting Serial Killers
- Learning to Love Complex Numbers
- Holidays and Homicide
- Numerical Integration
- Busy Beavers, and the Quest for Big Numbers
- Row Reduction over a Field
- Complete Sequences and Magic Tricks
- Well Orderings and Search

## Education

- Teaching Mathematics – Graph Theory
- Learning Programming – Finger-Painting and Killing Zombies
- Why There’s no Hitchhiker’s Guide to Mathematics